Human and planetary health implications of negative emissions technologies

Meeting the 1.5 °C target may require removing up to 1,000 Gtonne CO2 by 2100 with Negative Emissions Technologies (NETs). We evaluate the impacts of Direct Air Capture and Bioenergy with Carbon Capture and Storage (DACCS and BECCS), finding that removing 5.9 Gtonne/year CO2 can prevent <9·102 disability-adjusted life years per million people annually, relative to a baseline without NETs. Avoiding this health burden—similar to that of Parkinson’s—can save substantial externalities (≤148 US$/tonne CO2), comparable to the NETs levelized costs. The health co-benefits of BECCS, dependent on the biomass source, can exceed those of DACCS. Although both NETs can help to operate within the climate change and ocean acidification planetary boundaries, they may lead to trade-offs between Earth-system processes. Only DACCS can avert damage to the biosphere integrity without challenging other biophysical limits (impacts ≤2% of the safe operating space). The quantified NETs co-benefits can incentivize their adoption.


Supplementary results
The results we present here help better understand the findings described in the main manuscript.
1.1 Impact assessment

Health and environmental impacts without credits
We generated additional results without considering the health and environmental credits. Accordingly, the health and environmental impacts depicted in Supplementary Figures 1 and 2 exclude the impacts prevented by substituting the electricity from the global mix with the electricity generated in the BECCS scenarios, as well as the impacts prevented by replacing beneficiated iron ore and sand with the byproducts of the ex situ mineralization.
Comparing these results to the impacts shown in Figures 3 and 5 of the main manuscript (which account for the avoided impacts), we can see that the assumption that the generated electricity replaces electricity from the global mix has a substantial influence on the results; the scenarios are ranked differently according to the human health impacts if the electricity credits are omitted.

Health and environmental impacts of the in situ sequestration processes
Supplementary Figures 3 and 4 display the health and environmental impacts of the scenarios based on the studied in situ sequestration options (geological sequestration at high pressure and mineralization based on freshwater and seawater).
The scenarios relying on mineralization with seawater lead to the lowest health impacts because of their low electricity and freshwater requirements. Mineralization with freshwater is the most damaging sequestration option to human health in all the studied scenarios owing to the health impacts related to its high freshwater use.
The scenarios relying on geological sequestration at high pressure generate more impact across the studied Earth-system processes -excluding global freshwater use, for which mineralization with freshwater is the most detrimental sequestration option -because of its higher electricity requirements. The impact of the in situ mineralization processes is quite similar across all the Earth-system processes -excluding freshwater use -, irrespective of the water source.

Breakdown of health and environmental impacts
The health and environmental impacts attributed to the unit processes that integrate the NETs systems, and their inputs and outputs, are depicted in Supplementary Figures 5 and 6. The results of the HTLS-DACCS, LTSS-DACCS, BECCS0 and BEDACCS scenarios represent the average impacts estimated for the NETs deploying the three in situ sequestration options. Overall, the required energy and biomass are the principal contributors to the detrimental health and environmental impacts of the DACCS and BECCS scenarios, respectively. Supplementary Fig. 1. Health impacts, excluding the health credits of the produced electricity and the byproducts of the ex situ mineralization in the BECCS scenarios. a Contribution of environmental mechanisms to the total health impacts, expressed in Disability-Adjusted life years (DALYs) per million people per year. Scenarios 1-16 comprise High-Temperature Liquid Sorbent (HTLS) and Low-Temperature Solid Sorbent (LTSS) DACCS -powered by natural gas with carbon capture and storage (NG+CCS), wind, solar photovoltaic (PV), nuclear, geothermal (GEO), or the global electricity mix deployed in the SSP2-1.9 marker scenario without NETs -, the basic BECCS scenarios (BECCS0) deploying Miscanthus (MISC) or poplar (POP) -assuming either Soil Carbon Sequestration (SCS) or land-use change (LUC) -, the hybrid BEDACCS configurations integrating BECCS0 and LTSS-DACCS, and the BECCS scenarios where CO2 is mineralized ex situ (BECCS-EXSITU). Scenarios 1-16 are ranked by the total health impacts, scenario 1 is the best. We show the global burden of certain diseases in 2019 1 for reference. The black bars indicate the health impact range of the scenarios based on the in situ sequestration options, i.e., geological sequestration at high pressure and mineral carbonation with freshwater (upper bound) or seawater (lower bound). b Health externalities, expressed in US$2020 per gross tonne CO2 captured (scenarios 1- 16) or emitted (scenario 0). Fig. 2. Impacts on the Earth-system processes -excluding the environmental credits of the produced electricity and the byproducts of the ex situ mineralization in the BECCS scenarios -and ranking of scenarios by impacts on human health and the Earth system. a Impacts on Earth-system processes expressed as a percentage of the size of the Safe Operating Space (SOS). The impacts on the following Earth-system processes were assessed: climate change -considering atmospheric CO2 concentration (CC-CO2) and energy imbalance (CC-EI) as control variables -, ocean acidification (OA), terrestrial biosphere integrity (TBI), global biogeochemical flows -considering the application rate of intentionally fixed reactive nitrogen to the agricultural system (BGC-N) and phosphorus flows from freshwater into the ocean (BGC-P) as control variables -, global freshwater use (FWU), stratospheric ozone depletion (SOD), and global land-system change (LSC). Scenarios 1-16 comprise High-Temperature Liquid Sorbent (HTLS) and Low-Temperature Solid Sorbent (LTSS) DACCS -powered by natural gas with carbon capture and storage (NG+CCS), wind, solar photovoltaic (PV), nuclear, geothermal (GEO), or the global electricity mix deployed in the SSP2-1.9 marker scenario without NETs -, the basic BECCS scenarios (BECCS0) deploying Miscanthus (MISC) or poplar (POP) -assuming either Soil Carbon Sequestration (SCS) or land-use change (LUC) -, the hybrid BEDACCS configurations integrating BECCS0 and LTSS-DACCS, and the BECCS scenarios where CO2 is mineralized ex situ (BECCS-EXSITU). The values of empty cells range between 0 and 0.05%. We show the current level of the control variables for the Planetary Boundaries (PBs) of the studied Earth-system processes below using a qualitative color code, according to the PB framework. 2 b Ranking of scenarios by health impacts and maximum impacts across Earth-system processes relative to the SOS size, scenario 1 is the best.  Fig. 4. Impacts on the Earth-system processes -expressed as a percentage of the size of the Safe Operating Space (SOS) -of the scenarios based on the in situ sequestration alternatives: a Geological sequestration at high pressure. b Freshwater mineral carbonation. c Seawater mineral carbonation. The impacts on the following Earth-system processes were assessed: climate change -considering atmospheric CO2 concentration (CC-CO2) and energy imbalance (CC-EI) as control variables -, ocean acidification (OA), terrestrial biosphere integrity (TBI), global biogeochemical flows -considering the application rate of intentionally fixed reactive nitrogen to the agricultural system (BGC-N) and phosphorus flows from freshwater into the ocean (BGC-P) as control variables -, global freshwater use (FWU), stratospheric ozone depletion (SOD), and global land-system change (LSC). Scenarios 1-16 comprise High-Temperature Liquid Sorbent (HTLS) and Low-Temperature Solid Sorbent (LTSS) DACCS -powered by natural gas with carbon capture and storage (NG+CCS), wind, solar photovoltaic (PV), nuclear, geothermal (GEO), or the global electricity mix deployed in the SSP2-1.9 marker scenario without NETs -, the basic BECCS scenarios (BECCS0) deploying Miscanthus (MISC) or poplar (POP) -assuming either Soil Carbon Sequestration (SCS) or land-use change (LUC) -, the hybrid BEDACCS configurations integrating BECCS0 and LTSS-DACCS, and the BECCS scenarios where CO2 is mineralized ex situ (BECCS-EXSITU). We show the current level of the control variables for the Planetary Boundaries (PBs) of the studied Earth-system processes below using a color code, according to the PB framework. 2 The scenarios are ranked by the maximum impacts across Earth-system processes (average of sequestration alternatives), scenario 1 is the best. The values of empty cells range between 1·10 -4 and 0.08%.  Fig. 6. Breakdown of impacts on these Earth-system processes: a Climate change (control variable: CO2 concentration). b Climate change (control variable: energy imbalance). c Ocean acidification. d Terrestrial biosphere integrity. e Global biogeochemical flows (control variable: application rate of intentionally fixed reactive nitrogen to the agricultural system). f Global biogeochemical flows (control variable: phosphorus flows from freshwater into the ocean). g Global freshwater use. h Stratospheric ozone depletion. i Global land-system change. Scenarios 1-16 are ranked by the maximum impacts across Earth-system processes, expressed as a percentage of the size of the Safe Operating Space (SOS). Scenarios 1-16 comprise High-Temperature Liquid Sorbent (HTLS) and Low-Temperature Solid Sorbent (LTSS) DACCS -powered by natural gas with carbon capture and storage (NG+CCS), wind, solar photovoltaic (PV), nuclear, geothermal (GEO), or the global electricity mix deployed in the SSP2-1.9 marker scenario without NETs -, the basic BECCS scenarios (BECCS0) deploying Miscanthus (MISC) or poplar (POP) -assuming either Soil Carbon Sequestration (SCS) or landuse change (LUC) -, the hybrid BEDACCS configurations integrating BECCS0 and LTSS-DACCS, and the BECCS scenarios where CO2 is mineralized ex situ (BECCS-EXSITU). Scenario 1 is the best.

Externalities
Supplementary Figure 7 provides the health externalities of the NETs configurations based on the in situ sequestration options (geological sequestration at high pressure and in situ mineralization with freshwater or seawater).
Note that in the main manuscript, we only reported the externalities linked to human health.
Here we expand the analysis to cover the indirect costs associated with the other areas of protection, namely ecosystems quality and resource availability, to investigate whether they could offset the prevented health externalities. The externalities associated with the potential economic losses caused by climate change (e.g., infrastructure damaged due to extreme weather events, or the implementation of adaptation measures) are omitted from this assessment.
Supplementary Figure 8 shows the total monetized impacts of the studied NETs. Overall, the externalities associated with CO2 emissions can be reduced relative to the baseline with all the NETs except for the BECCS0 and BECCS-EXSITU configurations based on poplar, given their substantial impact on human health and ecosystems. While CDR prevents the harmful effects of CO2 on ecosystems, the extensive land use of BECCS leads to ecosystem damage and hence, additional externalities. On the contrary, the DACCS configurations reduce the impacts on ecosystems with respect to the baseline and thus, the associated externalities are negative.
The difference between the human health externalities and the total externalities varies across scenarios. This mismatch is minor in the LTSS-DACCS scenarios. However, more significant mismatches are observed for HTLS-DACCS -because of the large impact on resource availability associated with its natural gas consumption -and the BECCS configurations, due to the impacts of biomass cultivation on ecosystems.

CDR efficiency
Supplementary Table 1 shows the CO2 removal (CDR) efficiency (η CO 2 ) of the studied scenarios (quantified as the net kg CO2 removed per kg CO2 captured). These results were used to express the health and environmental impacts in terms of the functional unit.

Toxicity stressors
Supplementary

Life cycle models
This section describes the models used to compute the life cycle inventories of the assessed scenarios.

Direct Air Capture
In High-Temperature Liquid Sorbent Direct Air Capture (HTLS-DAC), atmospheric CO2 is absorbed into a basic solution, which is regenerated with high-temperature heat. The HTLS-DAC model is based on Carbon Engineering's DAC. 3 Here, natural gas supplies high-temperature heat, and the CO2 derived from the combustion of natural gas is captured and sequestered. In configuration 1 of HTLS-DAC, natural gas is burnt in a turbine to generate electricity. The emissions data of natural gas combustion were taken from the literature. 4,5 The second HTLS-DAC configuration uses electricity from the grid or a renewable energy source. The HTLS-DAC process is based on two connected chemical loops; thus, the intermediate chemical products must be temporarily stored when intermittent energy sources (wind or solar photovoltaic) are used.
In Low-Temperature Solid Sorbent Direct Air Capture (LTSS-DAC), CO2 is adsorbed onto a solid sorbent that is subsequently regenerated with low-temperature heat. 6 The energy consumption reported by Climeworks 7 was considered. Supplementary Table 3 shows the energy input of the studied DAC technologies (excluding the energy required to compress and sequester the CO2, which varies with the storage options).
Supplementary Table 3. Energy consumption of DAC, excluding transport and storage (kWh/tonne captured CO2). We studied two LTSS-DAC configurations. In the first one, the source of low-temperature heat is the excess heat generated in the production of geothermal electricity. As Supplementary Table  3 shows, the needed electricity to heat ratio is about 1 to 3, whereas the ratio of electricity to excess heat that can be recovered in the modeled geothermal plant is approximately 1 to 5. 8 We also considered the use of heat pumps based on working fluid R1234ze(E) to supply the lowtemperature heat (configuration 2). We estimated the coefficient of performance (COP) with equation S1, where T 1 is the temperature of the heat source (ambient air at 288 K) and T 2 represents the temperature required to desorb the CO2 (373 K). The efficiency of the heat pump (η hp ) is assumed to be 50%, which is within the typical range of efficiencies of industrial heat pumps. 9 With these data, we estimated a COP of 2.2, which leads to a total electricity consumption of 1,561 kWh/tonne CO2 captured for this LTSS-DAC configuration.

HTLS-DAC
The adsorbent consumption of the LTSS-DAC process is 7.5 kg/tonne. 10 The composition of the modeled adsorbent is 47.75% cellulose fiber, 47.75% polyethylenimine and 4.5% epoxy resin. 11 The production of polyethylenimine was modeled based on stoichiometric data and the typical yield (i.e., 87.5%) of the Wenker process. 12 The sodium sulfate generated as a byproduct of the process is assumed to be landfilled, whereas the unreacted products are treated in a hazardous waste incineration plant. Lacking more accurate estimates, the energy consumption of the Wenker process was approximated based on the average energy demand of a large multiproduct chemical plant, i.e., 3.2 MJ/kg (50% natural gas, 38% electricity and 12% steam). 13 The adsorbent is landfilled at the end of its lifetime.
The atmospheric water vapor retained in the adsorbent and subsequently desorbed with the low-temperature heat 14,15 is assumed to be released to the environment, without causing any impacts.

4.12
Supplementary Fig. 9. Carbon and energy flows between the foreground processes in the studied scenarios. a BECCS0. b BEDACCS. c BECCS-EXSITU.
The BECCS0 scenarios generate high-pressure (HP) and low-pressure (LP) steam. Part of the lowpressure (LP) steam is diverted from the turbine to supply the heat required to desorb the CO2 generated in the biomass combustion from the monoethanolamine (MEA) solution. In the BEDACCS scenarios, the remaining LP steam (the fraction not used to desorb the CO2 from the MEA solution) provides the low-temperature heat needed by the LTSS-DAC. Moreover, in the BECCS-EXSITU scenarios, part of the HP steam supplies the high-temperature heat required for the ex situ mineral carbonation. Since the energy content of the HP steam is fully exploited in the ex situ carbonation process, 26 there is insufficient LP steam to regenerate the MEA solution, and therefore 10-14% of the CO2 generated in the biomass combustion process is directly released into the atmosphere in the BECCS-EXSITU scenarios. The electricity consumed in the MEA capture unit, the LTSS-DAC and the ex situ mineralization constitutes an additional energy penalty for the bioenergy plant.

Transport and sequestration
The in situ mineral carbonation processes using freshwater and seawater consume 27 and 31 m 3 of water per tonne CO2 to dissolve the captured CO2, respectively. 27 The electricity required to pump the water into the basalt formation (E pump ) was estimated with equation S3, where V is the specific water volume that must be pumped, the pump isentropic efficiency (η pump ) is 0.8, and the motor efficiency (η pm ) equals 0.9. The water pressure is increased from P1 H 2 O (1 bar) to the injection pressure (P2 H 2 O ), i.e., 1.5 bar. 28 The captured CO2 must be compressed to be transported and injected into the geological reservoir (in the in situ sequestration options), or to react at the power plant with the magnesium extracted from the rocks (in the ex situ mineralization process). The CO2 pressures required for the different sequestration options are compiled in Supplementary Table 9. Due to the pressure drop that occurs during the CO2 transportation process (0.06 bar/km), 24 the transported CO2 must be recompressed prior to injection. The fugitive CO2 emissions associated with compression and transport are 2.90·10 -6 tonne/kWh and 7.33·10 -8 tonne/km/ton, 24 respectively.

Supplementary
Given the modular characteristics of DAC, 3,6 we assumed that the DACCS and BEDACCS plants are located next to the sequestration site regardless of the sequestration configuration. In situ mineralization requires a lower CO2 injection pressure than the conventional geological sequestration; consequently, its electricity consumption is lower. However, if the CO2 is transported, it must be compressed at a higher pressure than that required for the in situ mineralization. Therefore, we assume that the bioenergy plants are located next to the sequestration site in the scenarios deploying in situ and ex situ mineralization, and 400 km away from the sequestration point (CO2 transported at 150 bar by pipeline) in the configurations based on geological storage. We consider a conservative distance of 200 km (by road) from the biomass cultivation site to the power plant.
In the BECCS-EXSITU scenarios, the products of the ex situ mineral carbonation (magnesium carbonate and unreacted magnesium hydroxide) are used to backfill the mine from which the rock (serpentine) used in the ex situ mineralization process is extracted.
We did not consider any commercial applications for the product of the ex situ mineralization because, given the large scale at which the mineralization process is deployed, the chemical market is unlikely to be able to absorb it. 30 On the contrary, we expanded the system boundaries to consider the application of the byproducts of the carbonation process, assuming that the iron precipitated as FeOOH replaces the iron contained in beneficiated iron ore (65% iron), and that the produced silicon dioxide and the unreacted rocks replace sand used as an inert filler.
The mass balance of the ex situ mineralization process was carried out with the data derived from 26,31 . We estimated that 4.46 tonne rock are required to sequester 1 tonne CO2, based on the best magnesium conversion efficiency reported to date (56%), 32 and the following rock composition: 84% serpentine, 13% FeO and 3% CaSiO3. 31 Moreover, we assumed that the impacts of the rock mining activities are the same as those associated with the operation of an iron mine.
Based on the data reported by 26,31,33 , a heat requirement of 4.95 GJ/tonne CO2 was estimated for the ex situ mineralization process with the studied magnesium conversion efficiency. The electricity consumed to crush and grind the rocks to 100 µm 34 is 13.40 kWh/tonne. 35

Electricity mix
We estimated the average contribution of energy source es to the global electricity mix deployed in the SSP2-1.9 marker scenario between 2030 and 2100 (AVMIX es ) with equation S5, where MIX es,t represents the fraction of energy source es in the electricity mix of year t, and CDR t , the CDR rate.
Supplementary Table 11 shows the CDR rates and the contributions of the deployed energy sources to the electricity mix across the studied period. 36 In the HTLS-and LTSS-DACCS scenarios, we assume that BECCS is not deployed. Moreover, the electricity generated in the BECCS scenarios replaces the electricity produced with other technologies. Therefore, AVMIX es does not include the contribution of BECCS to the mix, i.e., AVMIX es=BECCS = 0. The shares of each energy source are re-scaled to sum up 100% after removing the BECCS contribution.

Potential deployment constraints
Supplementary Table 12 compares the energy required to remove 5.9 net Gtonne/year CO2 (scenario SSP2-1.9) via LTSS-DAC coupled to geological sequestration -the DACCS configuration with the highest consumption of renewable energy -to the ranges of global technical potentials estimated for renewable energy sources. 37 The required energy inputs are below the maximum technical potentials estimated for the assessed energy sources, confirming the technical feasibility of the proposed configurations. We also evaluated the total area of grassland needed to fulfill the functional unit in scenarios BECCS-EXSITU-MISC and BECCS-EXSITU-POP -those with the largest biomass consumptionagainst the current global area of natural and semi-natural grasslands (6.7·10 6 km 2 ). 39 We estimated that scenario BECCS-EXSITU-MISC and BECCS-EXSITU-POP would require 2.1 and 3.9% of the current global grassland area, respectively.

Supplementary
Finally, it has been estimated that the global reserves of serpentine are sufficient to sequester global CO2 emissions, 40 whereas basaltic rocks are widely abundant on the Earth's surface. 41 Therefore, rock availability will not act as a bottleneck for the large-scale deployment of the mineral carbonation processes.

Supplementary methods
Here we describe the methods used to evaluate the human health and Earth-system impacts, and the externalities.

Health damage factors of CO2 emissions
Supplementary Table 13 compiles the breakdown of the damage factors used to calculate the climate-related health impacts by health risk and region for SSP2. 42 The countries and territories comprised within each region are displayed in Supplementary Table 14. Supplementary

Estimation of externalities
We monetized the human health impacts linked to the capture of 1 tonne CO2 by applying the conversion factor proposed by Weidema (1 DALY = 74,000 €2003) -43 to the non-climate and climate-related health impacts, which were estimated with the ReCiPe 2016 endpoint method 44 (Hierarchist perspective) and the health damage factors provided by Tang et al. 42 for SSP2, respectively.
We also estimated the externalities associated with the damage to the other areas of protection differentiated within the ReCiPe 2016 endpoint method, i.e., ecosystem quality and resource availability. We applied the following equivalence: 1 lost species·year = 9.5·10 6 €2003 to translate the damage to ecosystems calculated with the ReCiPe Hierarchist perspective into monetary units. 43 The ReCiPe 2016 endpoint method expresses damage to resource availability in US$2013. We used the currency conversion factors and GDP deflators found in 45,46 to express the monetary units in US$2020.
The externalities were compared to the levelized CO2 cost of scaled-up HTLS-DACCS (181-249 US$/tonne for configuration 1 and 121-175 US$/tonne for configuration 2) 3 and combustion BECCS (134-188 US$/tonne). 20 The levelized CO2 cost of BECCS was estimated by subtracting the electricity revenues -assuming an electricity selling price of 130 €/MWh 47 -from the total BECCS costs provided in 20 and adjusted for inflation. 46 The levelized CO2 cost of LTSS-DACCS is currently about 600 US$/tonne 48 , although Climeworks expects the cost to drop to approximately 100 US$/tonne by 2030. 6

Earth-system impact assessment
To conduct the Earth-system impact assessment, we adjusted some of the characterization factors described in 49 , as Supplementary Table 15 shows. To calculate the characterization factors used to estimate the climate change and ocean acidification impacts of the CO2 from land transformation environmental flow, Ryberg et al. 49 divided the CO2 characterization factors by the time horizon (300 years). They did that under the assumption that this elementary flow appears in the inventories as a pulse emission that must be annualized. However, the CO2 emissions due to LUC that occur in the foreground systems are already annualized in our model (equation S2). Likewise, the CO2 emissions from land transformation provided by the Ecoinvent processes are calculated based on the annual change in Soil Organic Carbon, following the IPCC recommendations. 17 Hence, we applied the characterization factors of CO2 to the CO2 from land transformation environmental flow, consistently with other impact assessment methods (e.g., IPCC 2013, 50 ReCiPe 2016 44 ).

Supplementary
We defined a characterization factor for PO4 3--calculated as the product of the P characterization factor (freshwater emission compartment) and the mass fraction of P in PO4 3--to estimate the impact on the P flow. We also defined a characterization factor to account for the contribution of N2O to stratospheric ozone depletion, as suggested in Algunaibet et al. 51 The characterization factors developed by Ryberg et al. 49 to estimate the impacts on the N flow require special attention. First, the life cycle assessment practitioner must select only one of the main environmental compartments where emissions occur to avoid double accounting, since emissions of N to different compartments can be due to the same amount of N fixed. Second, these characterization factors are calculated via inverse modeling and based on global parameters. However, they should be site-specific, depending on local conditions such as soil properties.
To produce more accurate estimates, we directly calculated the total amount of N fixed in the following Ecoinvent activities, which are part of the supply chains of the assessed systems: Ammonium nitrate, as N|ammonium nitrate production Ammonium nitrate, as N|calcium nitrate production Ammonium sulfate, as N|ammonium sulfate production Nitrogen fertilizer, as N|ammonium nitrate phosphate production Nitrogen fertilizer, as N|calcium ammonium nitrate production Nitrogen fertilizer, as N|diammonium phosphate production Nitrogen fertilizer, as N|monoammonium phosphate production Nitrogen fertilizer, as N|urea ammonium nitrate production Urea, as N|production Nitrogen fertilizer, as N|nutrient supply from ammonium chloride Nitrogen fertilizer, as N|nutrient supply from calcium nitrate Nitrogen fertilizer, as N|nutrient supply from potassium nitrate These activities were selected in accordance with the definition of the N Planetary Boundary (PB) control variable, i.e., the application rate of intentionally fixed N in the agricultural system. 2 Therefore, the activities fixing N for non-agricultural purposes must be excluded from the analysis of the impacts on the N flow. In our study, we only omitted the N linked to the ammonium sulfate used in the ex situ mineral carbonation process from the above-mentioned list of activities. Hence, this approach -like the method developed by Ryberg et al. 49 -might be overestimating the impacts, because some of these products could have non-agricultural applications in the background processes, e.g., in mining activities.
Supplementary Table 16 compiles the values of the PBs, the natural background (NB) and the full Safe Operating Space (SOS) of the assessed Earth-system processes, obtained from 2,49 . According to Bouwman et al. 52 -the source used by de Vries et al. 53 to estimate the N PB -, 68% of the intentionally fixed N in the agricultural system is associated with industrial fertilizers, and 32% is biologically fixed. Since our models do not account for the biologically fixed N, the value of the N PB provided by Steffen et al. 2 was multiplied by 0.68 to define the N PB for industrial fertilizers.

Assumptions and limitations
Here we list the main assumptions and limitations of our life cycle models and the impact assessment methods.

Life cycle models
In accordance with the recommended guidelines for prospective life cycle assessment studies, emerging technologies in early development stages modeled at a large-scale deployment level should avoid temporal mismatches between the background and foreground activities. 54 Background activities are described with homogenous data based on average market values, while foreground activities are specific to the studied system. 55 However, modeling all the background activities and the structural market changes that may result from deploying Negative Emissions Technologies (NETs) at a large scale would require making additional assumptions regarding the evolution of future technologies, thereby resulting in more pronounced uncertainties. Hence, the background activities of our scenarios, including electricity generation, rely on the current average market mixes.
We compared the health and environmental impacts of the 2018 global electricity mix (composition taken from the IEA 56 ) and the future electricity mix used here for the foreground activities (Supplementary Tables 17 and 18) to assess how changing the electricity mix in the background activities would affect our analysis. We found that, although increasing the share of nuclear energy would lead to higher health impacts linked to ionizing radiation, the overall health and environmental impacts of the future decarbonized mix would be lower. Accordingly, our results represent conservative estimates.
Another limitation of the study is that we did not conduct a regionalized analysis. However, the health impacts linked to ozone formation, water consumption, fine particulate matter formation and toxicity vary across different regions. Furthermore, additional trade-offs between the PBs operating at regional scales (the regional phosphorus PB, the land-system change PBs identified for different biomes, the basin-scale PB for freshwater withdrawal, and the regional atmospheric aerosol loading PBs) 2 could arise.

Impact assessment method
We only quantified the climate-sensitive health impacts related to a subset of health risks, namely undernutrition, malaria, coastal floods, diarrhea, heat stress and dengue. 42 On the other hand, the method used to estimate the impacts on the terrestrial biosphere 57 only considers two main stressors, namely greenhouse gas emissions and land use. 58,59 Therefore, the averted climate-sensitive health effects and the impacts on the terrestrial biosphere could be higher. Conversely, we could be overestimating the impact on the N flow Earth-system process because some of the products responsible for N fixation in the background system may have nonagricultural applications and thus may not affect the N PB control variable.
The damage to the biosphere integrity and the health impacts are aggregated over a 100-year time horizon, following the consensus scientific models. 44 Nevertheless, the life cycle impact assessment method used to quantify the climate change and ocean acidification impacts based on the PB framework considers a 300-year time horizon because the model used to derive the climate change characterization factors attains the stabilization of the atmospheric CO2 concentration at a level similar to that of the climate change PB over a 300-year period. 49 Thus, shorter time horizons would lead to results that do not reflect the level of greenhouse gas emissions that allows humanity to operate within the SOS of the climate change Earth-system process.